UNITED NATIONS, June 14 (Reuters/Louis Charbonneau) - The United Nations said on Monday that Ban Ki-moon took note of Israel's announcement about its probe of a recent deadly raid on a Gaza aid flotilla but continued to push for a full international investigation.

Israel's cabinet approved an Israeli inquiry into the May 31 raid, which left nine protesters dead. It responded to international demands for impartiality by putting two foreign observers on the panel.

A thorough Israeli investigation is important and could fit with the secretary-general's proposal, which would fully meet the international community's expectation for a credible and impartial investigation, he said.

But Haq added that Ban's proposal for an international inquiry remains on the table and he hopes for a positive Israeli response. He said Israel had not rejected Ban's idea.

Diplomats say Ban has urged Israel to accept a neutral inquiry panel led by former New Zealand Prime Minister Geoffrey Palmer and the cautious UN reaction may indicate that Ban had doubts about whether an Israeli-led probe would suffice.

Angered by the killing by Israeli commandos of nine Turkish pro-Palestinian activists on May 31, Turkey said an Israeli investigation would be biased and reiterated demands for a UN-controlled probe.

Israel's close ally the United States backed a June 1 UN Security Council statement that called for a prompt, impartial, credible and transparent investigation conforming to international standards.

Diplomats familiar with Ban's proposal said he suggested Palmer could have two deputies, one from Israel and another from Turkey. Israel has responded coolly to Ban's idea.

UN diplomats say it is clear that Israel opposes a UN-led investigation. The main reason is the Israeli view that a UN Human Rights Council-mandated inquiry into the December 2008-January 2009 war in the Gaza Strip led by South African jurist Richard Goldstone did serious damage to Israel.

The Goldstone Report accused both Israel and Hamas militants who control Gaza of war crimes, charges the Israelis and Hamas rejected.

At least four separate inquiries into the flotilla incident have been proposed, including the Israeli probe and Ban's inquiry. Turkish authorities have to carry out their own investigation because Turkish nationals were killed. The Human Rights Council has also said it would organize its own fact-finding mission.